A senior Obama State Department official gave the green light to an FBI agent in 2016 to meet with dossier writer Christopher Steele, a new book says.

The two met at Mr. Steele’s London office, touching off a relationship that would fuel the ongoing investigation into possible Donald Trump-Russia election collusion that shows no sign of ending.

Mr. Steele’s sensational charge that prompted an FBI wiretap on Trump volunteer Carter Page was sourced to the girlfriend of an unidentified Kremlin figure, according to the book. Republicans have roundly criticized the bureau for relying on the unverified, Democratic Party-financed dossier to ask a judge to approve a year of surveillance in 2016 and 2017.

John O. Brennan, Mr. Obama’s CIA director, worked behind the scenes before the election to get his suspicions about Trump and Russia into the news media.

These disclosures, including that Victoria Nuland, then at State, started the FBI-Steele marriage is contained in “Russian Roulette.” The book, which was released Tuesday, was authored by two longtime Washington media figures: Yahoo News reporter Michael Isikoff and Mother Jones magazine’s David Corn.

Two committees, the House Permanent Select Committee on Intelligence and the Senate Judiciary Committee, are investigating how Obama officials promoted Mr. Steele’s 35-page dossier, which in essence is raw opposition research designed to destroy the Trump candidacy.

Mr. Steele makes a series of criminal charges against Mr. Trump and his associates, contending there was an “extensive conspiracy” between them and the Kremlin. This supposed collusion has not been substantiated publicly. House intelligence committee Republicans on Monday said their 14-month investigation found no collusion and had ended.

“Russian Roulette” shows Obama people played a role in promoting the collusion theory and getting law enforcement involved.

Mr. Steele was excited over his findings about Mr. Trump’s supposed dalliance with Russian prostitutes and purported collusion with the Kremlin. He pressed his handler, Glenn Simpson of Fusion GPS, to let him go to the FBI.

Mr. Simpson agreed. Mr. Steele telephoned Michael Gaeta, an FBI agent with whom he worked on soccer league corruption who was then stationed at the U.S. Embassy in Rome.

“I can’t discuss it over the phone. You have to come here. Believe me, Mike, you have to come to London,” Mr. Steele told him that summer.

Says “Russian Roulette,” “There were a few hoops Gaeta had to jump through. He was assigned to the U.S. embassy in Rome. The FBI checked with Victoria Nuland’s office at the State Department: Do you support this meeting? Nuland, having found Steele’s reports on Ukraine to have been generally credible, gave the green light.”

“Within a few days, on July 5, Gaeta arrived and headed to Steele’s office near Victoria station. Steele handed him a copy of the report. Gaeta, a seasoned FBI agent, started to read. He turned white. For a while, Gaeta said nothing. Then he remarked, ‘I have to report this to headquarters.’”

Ms. Nuland’s name surfaced in January as Senate investigators under Senate Judiciary Committee Chairman Chuck Grassley, Iowa Republican, turned up evidence that Mr. Steele met with another Obama State Department official, Jonathan Winer.

He worked as a middleman to bring Mr. Steele together with Sidney Blumenthal, a fierce Hillary Clinton defender. Mr. Winer spoke with Ms. Nuland, who gave a heads-up to Secretary of State John F. Kerry.

At the time, Ms. Nuland, a career diplomat, was assistant secretary of state for European and Eurasian affairs.

She is now chief executive at the Center for a New American Security. A message to the press office was not returned.

In the Page affair, Mr. Steele accused the energy investor of meeting with two Kremlin figures while in Moscow to deliver a public speech in July 2016. Mr. Steele said the three discussed bribes for sanctions relief.

Mr. Page has testified under oath that he never met the two men or discussed bribes.

Ms. Nuland was not the only Obama appointee working against the Trump candidate.

Isikoff-Corn report that Mr. Brennan, who in retirement is one of Mr. Trump’s hardest critics, telephoned Senate Minority Leader Harry Reid, Nevada Democrat, in August 2016. He alerted him that Russia had hacked Democrat Party computers and suggested that the Trump campaign was in on the plot. This charge has not been substantiated more than a year later.

Mr. Brennan’s call was to prompt Mr. Reid to expose the news publicly, which he did. His open letter referred, without name, to the Page trip, something right out of the dossier, which had not yet become public.

The authors say the information likely came from the Clinton campaign, which had been briefed on Mr. Steele’s allegations. Mr. Steele was paid by Fusion with money from the Democratic National Committee and Hillary Clinton campaign. Republicans have called this collusion — using bought smut from Russian sources to inject into the campaign.

“Russian Roulette” picks up many Democratic Party talking points.

⦁ Democrats are portrayed as truth-seekers while Trump people are awash in Russian contacts.

⦁ Mr. Steele’s sensational charges are repeated with not much skepticism.

⦁ Mr. Steele is possibly the most respected spy in recent British history.

⦁ The Trump transition team may have been violating the obscure 1799 Logan Act by conducting diplomacy. This charge was spun to reporters from the Obama Justice Department.

As the Nov. 8 election lay days away, Mr. Simpson, who was desperate to get Steele’s anti-Trump narratives into the media, met with Mr. Corn over the former spy’s latest anti-Trump memo.

” ‘This stuff is almost unbelievable,’ Simpson said,” according to the book.